Alexandria Engineering Journal (2016) xxx, xxx–xxx

HO ST E D BY

Alexandria University

Alexandria Engineering Journal

www.elsevier.com/locate/aejwww.sciencedirect.com

ORIGINAL ARTICLE

Short Circuit Stress Analysis Using FEM in Power

Transformer on H-V Winding Displaced Vertically

& Horizontally

* Corresponding author.E-mail addresses: ashfaqahmad83@hotmail.com, ashfaq.ahmad@es.

uol.edu.pk (A. Ahmad).

Peer review under responsibility of Faculty of Engineering, Alexandria

University.

http://dx.doi.org/10.1016/j.aej.2016.10.0061110-0168 � 2016 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V.This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Please cite this article in press as: A. Ahmad et al., Short Circuit Stress Analysis Using FEM in Power Transformer on H-V Winding Displaced Verticallyizontally, Alexandria Eng. J. (2016), http://dx.doi.org/10.1016/j.aej.2016.10.006

Ashfaq Ahmada,*, Iqra Javed

b, Waseem Nazar

a, M. Asim Mukhtar

a

aThe University of Lahore, Department of Electronics, 1-km Raiwind Road, Lahore, PakistanbUniversity of Management and Technology, Department of Informatics and Systems, Lahore, Pakistan

Received 24 August 2016; revised 14 October 2016; accepted 17 October 2016

KEYWORDS

Finite element method;

Power transformer;

Short circuit stress;

Mechanical stresses;

Axial and radial stresses;

High voltage winding

Abstract The aim of this work was to work out the mechanical stresses within transformer result-

ing from the extreme short-circuit currents. The forces and stresses set up in transformer windings

as the result of exterior or interior short-circuits or of switching operations, are measured in detail.

A variety of arrangements of windings in large power transformers are described. Points at which

mostly high mechanical stresses take place in concentric windings are discussed in detail. Analytical

and FEM calculations for individual short circuit forces, axial and radial have been discussed. The

result was then compared with actual measurements on a prototype 20 MVA 132/11.5 kV power

transformer [15]. Various failure mechanisms due to these forces have been discussed. Design

parameters are also discussed, whose values determine the maximum stresses which may occur in

any part of the transformer. Effects of irregularity in various parts and various properties of mate-

rials have been studied and the usage of appropriate material for withstanding the dynamic effects

of SC is discussed. Effect of workmanship errors on short circuit withstand capability has also elu-

cidated. Finally, a complete model is developed.� 2016 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V. This is an

open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

1. Introduction

Nowadays transformer failures are increasing day by day

which is a serious problem for a country like Pakistan facingthe energy crisis. The major cause of transformer failure inpower system is short circuit faults. Most of the transformers

fail during the short circuit test which has become a major con-cern for the manufacturers.

Power transformers are critical and expensive componentsof the energy transmission and distribution process for electricutilities. It may be noted that about 33% of failures are due tothe windings faults.

Power transformers are one of the main devices in foundpower systems. Reliability, power quality and economic costare affected by the transformer’s health conditions. Catas-

trophic failures of power transformers may have a seriousenvironmental impact, such as fire and transformer oil spill.

& Hor-

Figure 1 A sinusoidal voltage source switched on to an RL

network.

2 A. Ahmad et al.

Therefore, the failures of power transformers are of much con-cern and are investigated extensively [1,2].

Lack of strengthening of transformers (for short-circuit

proofness) by manufacturers can cause severe damages to thetransformer as well as the system, prominent of which are asfollows:

� Deformation of LV and HV windings.� Broken pressure plates on windings.

� Bending of clamping structure.� Bulging of tank body.� Collapse of bushings.� Short-Circuited tapping leads.

As a result, development of condition monitoring systemsfor the winding of power transformers holds promise toward

cost reduction throughout power transformers’ life cycle andtoward an increase in the availability and reliability of powertransformers.

In this paper, some basic theoretical backgrounds of short-circuit’s stresses are given, especially with respect to powertransformers. The three different types of mechanical forces

that arise in the windings during short-circuit are evaluatedmainly the Axial Forces, Radial Forces and the combinationof (axial and radial) stresses at the winding ends.

Calculation of these forces using the Finite Element

Method was performed. Design parameters are discussed,whose values determine the maximum stresses which mayoccur in any part of the transformer. Effects of asymmetry

in various parts are also studied. Different properties of mate-rials are studied and the usage of proper material for with-standing the dynamic effect of short-circuits is studied too.

Effect of workmanship errors on short-circuit withstand capa-bility is also elucidated. Finally, a complete model for thestudy of dynamic effects of short-circuits in a power trans-

former is developed.

2. Short circuit currents

Almost all types of faults cause the sudden rise of current inpower system which results in malfunction and inconsistentoperation of installed equipment along with severe effect ontransformer insulation. Usually, the three-phase faults are

the most severe of all; hence, the transformer should bedesigned to withstand the effects of symmetrical three phasefaults. It must be mentioned here that in some cases (where

a tertiary connected winding is present), the single-phase toline fault short-circuit current can be higher than the three-phase fault on those windings, since it is related to very special

cases, emphasis is made on symmetrical three-phase faultsonly.

2.1. Value of symmetrical short-circuit current

For three-phase transformers with two separate windings, ther.m.s. value of the symmetrical short-circuits current ‘‘I” shallbe calculated as in Eq. (i) [4].

I ¼ Uffiffiffi3

p � ðZt þ ZsÞðiÞ

where

Please cite this article in press as: A. Ahmad et al., Short Circuit Stress Analysis Usizontally, Alexandria Eng. J. (2016), http://dx.doi.org/10.1016/j.aej.2016.10.006

U: is the rated voltage of the winding under consideration,

in kilovolts,Zt: is the short-circuit impedance of the transformerreferred to the winding under consideration, in ohms perphases,

Zs: is the short-circuit impedance of the system, in ohms perphase.

As mentioned above, due to addition of more and moregenerating stations within an interconnected system, the sourceimpedance Zs is very small and generally neglected for calcula-

tions purpose.

2.2. Nature of short-circuit current

Consider the circuit given alternate voltage source. Assuming

that the below with an switch is closed at t= 0 instant, whichsimulates the short-circuit, the expression for the current i(t)can be written as follows (see Fig. 1):

iðtÞ ¼ Imax½sinð�xt� hÞ� ðiiÞwhere

Imax: maximum value of the current i,

t: time, in seconds,h: phase angle of the circuit impedance [tan � 1(uL/R)],

s: time constant [L/R].

The plot of this current expression with respect to time is asshown in Fig. 2.

The mechanical strength of the transformer windingsshould be such that it shall withstand the highest short-circuit forces generated which correspond to the first current

peak in the figure above, since this current peak has the highestmagnitude due to the presence of DC component in the cur-rent pattern [8,9].

3. Short-circuit forces

When a current carrying conductor lies in a magnetic field, a

force is produced upon that current carrying conductor, whosemagnitude is given by Eq. (iii).

F ¼ B � I � L sin a ðiiiÞwhere

ing FEM in Power Transformer on H-V Winding Displaced Vertically & Hor-

Figure 2 The shape of a transient in an inductive circuit.

Figure 3 Geometry of the transformer.

Short Circuit Stress Analysis 3

B: flux density, in Tesla,

I: current in the conductor, in Amps,L: length of current carrying element, in meters,a: angle between flux density vector and current vector.

This force is called the ‘‘electromagnetic” force because it isproduced by both combined effect or electric current and mag-

netic flux [12,10]. The direction of this force can be easily com-puted using the well-Known ‘‘Left-hand rule”.

3.1. Electromagnetic forces

In transformers, electromagnetic forces may have three com-ponents if we model it in 3D cylindrical coordinates.

� r-component.� z-component.� /-component.

The r-component of the electromagnetic forces results inthe radial forces that act on the windings [8]. The z-

component is the originator of the axial forces that act onthe windings. Finally, the /-component can cause twistingmotion of the windings, but it is never present because of the

other. The conventional way to calculate the short-circuitforces is by solving Eq. (iii), using data of the transformer fromthe design calculation sheets. This calculation, however,assumes a lot of data which can sometimes result in a very safe

calculation and, elsewise, could result in unsafe margins duringcalculations [3].

4. Center axis of the windings is always coinciding with each

finite element modeling

4.1. Introduction to finite element method

Finite element method (FEM) is a numerical method mainly

used for solving Differential and Integral equations. Essenceof this method is to divide the application domain in very smallsub domain elements called as finite elements. Problem is sub-

divided into Finite size sub problems and is independentlydealt to find complete problem solution.

There are many software commercially available incorpo-rating the Finite Element Method Solution. In this paper, a

software tool titled meshing and finite element solver has beenused [1]. The model has been drawn using MATLAB with

Please cite this article in press as: A. Ahmad et al., Short Circuit Stress Analysis Usizontally, Alexandria Eng. J. (2016), http://dx.doi.org/10.1016/j.aej.2016.10.006

complete computation of leakage flux and therefore short-circuit forces.

4.2. Finite element method in transformer

In transformers, finite element method can be used to calculatethe following quantities:

� Eddy currents and winding stray losses.� Electric field analysis.

� Temperature gradient calculations.� Short-circuit stresses.� Stress-strain analysis of the clamping structure.

4.3. Steps of finite element modeling

Finite Element modeling is a highly accurate method of calcu-

lating the transformer parameters. The FEM formation makesuse of the fact that Poisson’s partial-differential equation issatisfied when total magnetic energy function is a minimum

[4,5].

1. The geometry to solve (which is basically the core and set of

transformer windings represented simple as rectangularblocks) can be drawn using most CAD programs. In thiswork, Auto Cad 2010 is used to draw the geometry in .dxf format (see Fig. 3).

2. Once the geometry is ready, it is then divided into finite ele-ments i.e. small elements. The smaller the size of each meshor element, the higher will be the accuracy of the results can

be obtained if problem is divided into number of smallproblems. Different models and geometries of transformerfor the application and calculations are given in Figs. 4–

ing FEM in Power Transformer on H-V Winding Displaced Vertically & Hor-

Figure 5 Flux pattern of a transformer.

4 A. Ahmad et al.

7, while Figs. 8 and 9 show flux plots of transformer which

are important to obtain while calculating short circuit effecton power transformer windings.

3. The properties of each of the blocks drawn, are then

assigned along with the boundary conditions. Since corehas a very high relative permeability value, it will not storeany appreciable energy. Hence, it doesn’t matter whethercore is given a relative permeability of 10,000 or 100,000.

When assigning the properties to the windings, it must bemade sure that the ampere-turns of all the winding regimesmust be equal and opposite, so that no mutual component

of flux in the core should exist.4. The space filled with oil is assigned a relative permeability

of 1, including the windings.

5. The geometry is solved in the FEM solver and the flux leak-age plot obtained.

5. Analysis on stresses based on vertical movement

Analysis of HV winding in vertical of power transformer was

performed.The winding rotation steps were chosen arbitrary as per

design approach. The movement step is 0-mm, 2-mm, 5-mm,10-mm, 15-mm is chosen for vertical respectively.

The results and geometry model for these movements aregiven in Fig. 6.

Fig. 7 shows mesh model in these cases would be displaced

in vertically as shown below.The geometries are solved in the FEM solver software and

the flux leakage plots obtained as in Fig. 8.

Following is the comprehensive simulation results of fluxesobtained from FEM measured forces obtained from FEMMby setting properties of core, oil, LV, HV windings, etc. It alsoincludes comparison plots of forces obtained by MATLAB.

Figure 4 Meshing of the transformer geometry.

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There are number of findings from the simulation results ofFEMM.

� The direction of short-circuit flux (arrows in the figure).� Total effect of the forces appears to cancel out.

� Forces at the winding center are purely radial.� Inner winding is subject to buckling effect.� Outer winding tends to stretch out.

� Forces at the winding ends have both axial and radial direc-tions [7,11].

The flux simulation results at vertical movement are given

below which are extracted from [6,7]. The minimum flux den-sity is shown with light color while maximum flux density ispresent at top middle and bottom turns of winding. Different

colors show the level of flux produced in windings followed bymeasurement of H.V and L.V forces at bottom and in differentpositions in windings with the help of FEM. Results are con-

cluded by comparing the results of FEMM and measurementsmade mathematically. In given below flux density plots as inFig. 9, various levels of flux densities are presented by different

colors [13].

6. Vertical winding forces

The comparison plot of LV forces in windings at different dis-placements is given in Fig. 10.

From the above plot in Fig. 10, it is clear that in early turnsthe negative forces are dominant and in middle of the turns the

forces approach to zero because of cancelation of effect of thenegative and positive forces. This force applied on windingpattern is same for the displacements of 0-mm, 2-mm, 4-mm,

ing FEM in Power Transformer on H-V Winding Displaced Vertically & Hor-

Figure 6 Geometrical model.

Figure 7 Mesh model.

Figure 8 Flux plot.

Short Circuit Stress Analysis 5

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Figure 9 Flux density plot.

Figure 10 Comparison of LV forces in winding.

6 A. Ahmad et al.

5-mm, 6-mm, 8-mm, 10-mm and 15-mm. The only difference is

the windings having less displacement have tendency of nega-tive forces to approach from negative to zero more quickly andforces approach from zero to positive more slowly and vice

versa. The comparison plot of HV forces in windings at differ-ent displacements is given in Fig. 11.

From above plot it is clear that in early turns the negativeforces are dominant and in middle of the turns the forces

approach to zero because of cancelation of effect of the nega-tive and positive forces. This force applied on winding patternis same for the displacements of 0-mm, 2-mm, 4-mm, 5-mm, 6-

mm, 8-mm, 10-mm and 15-mm. The only difference is thewindings having less displacement have tendency of negativeforces to approach from negative to zero more quickly and

forces approach from zero to positive more slowly and viceversa. Figs. 10 and 11 show the complete comparison plotsof LV and HV forces in windings at different displacements.Figs. 12 and 13 show the individual plots of forces in winding

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at different displacements 0-mm, 2-mm, 4-mm, 5-mm, 6-mm,

8-mm, 10-mm and 15-mm respectively.

6.1. x-axis forces at winding

The comparison plot of LV forces at bottom of windings atdifferent displacements is given in Fig. 14.

From the above plot it is clear that accumulated forces areminimal in upper and bottom turns, whereas accumulated

force is maximum at middle turns of windings. The accumu-lated force increases from zero to a constant maximum valueearlier at winding having less displacement and decreases from

maximum value to zero late in bottom turns and vice versa forwindings with more displacement. This force applied on wind-ing pattern is same for the displacements of 0-mm, 2-mm, 4-

mm, 5-mm, 6-mm, 8-mm, 10-mm and 15-mm. The comparisonplot of HV forces at bottom of windings at different displace-ments is given in Fig. 15.

ing FEM in Power Transformer on H-V Winding Displaced Vertically & Hor-

Figure 11 Comparison of HV forces in windings.

Figure 12 Individual LV forces in winding at different displacements.

Short Circuit Stress Analysis 7

From the above plot it is clear that accumulated forces areminimal in upper and bottom turns, whereas accumulatedforce is maximum at middle turns of windings. The accumu-

lated force increases from zero to a constant maximum valueearlier at winding having less displacement and decreases frommaximum value to zero late in bottom turns and vice versa for

windings with more displacement. This force applied on wind-ing pattern is same for the displacements of 0-mm, 2-mm, 4-mm, 5-mm, 6-mm, 8-mm, 10-mm and 15-mm. Figs. 16 and17 show the individual plots of forces at winding on different

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displacements 0-mm, 2-mm, 4-mm, 5-mm, 6-mm, 8-mm, 10-mm and 15-mm.

7. Short circuit forces experimental value and theoretical value

with percentage error

In this paper we displaced high voltage winding of the trans-

former on both axes (horizontally and vertically). The dis-placed points are discussed above in this paper. We calculatethe percentage error for all displaced transformers. Finally plot

ing FEM in Power Transformer on H-V Winding Displaced Vertically & Hor-

Figure 13 Individual HV forces in winding at different displacements.

Figure 14 Comparison of LV forces at windings.

8 A. Ahmad et al.

the percentage error graph versus displaced values of trans-former winding.

Fax ¼ 0:6289ðN � IÞ2ðHwÞ2

� p �Dm � dþ a1 þ a23

� �� ð2K� 1Þr2

� ðKffiffiffi2

pÞ2 � 10�6N

Hw = geometrical average length of windings,

N= number of turns,I= current of HV,

Dm =mean diameter of the pair of windings,

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d = width of main duct,

a1 & a2 = radial width of winding # 1 & 2,K =Rogowski factor.

For LV : Dm1 ¼ outer diameter� inner diameter

2

For HV : Dm2 ¼ outer diameter� inner diameter

2

ing FEM in Power Transformer on H-V Winding Displaced Vertically & Hor-

Figure 15 Comparison of HV forces at windings.

Figure 16 Individual LV forces at winding on different displacements.

Short Circuit Stress Analysis 9

Dm ¼ Dm1þDm2

2; K ¼ 1� dþ a1 þ a2

p �Hw

Given data:HV current = 1287.878788,

Outer diameter of LV = 658 mm; inner diameter of

LV = 535 mm,Outer diameter of HV= 946 mm; inner diameter ofHV= 742 mm,

N= 2067,r= 3.2 mm,

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d= 42 mm,a1 = 61.5 mm,a2 = 102 mm,

Hw = 1324 mm.

0-mm:

K ¼ 1� 42þ 61:5þ 102

3:14� 1324¼ 0:950

Dm1 ¼ 658� 535

2¼ 61:5; Dm2 ¼ 946� 742

2¼ 102

ing FEM in Power Transformer on H-V Winding Displaced Vertically & Hor-

Figure 17 Individual HV forces at winding on different displacements.

10 A. Ahmad et al.

Dm ¼ Dm1þDm2

2¼ 61:5þ 102

2¼ 81:75

r2 ¼ 10;ffiffiffi2

p¼ 1:414

Table 1 Percentage error value.

Sr # Displacements (mm) Percentage errors (%)

1 0 7.72

2 2 5.5

3 4 3.43

4 5 2.64

5 6 1.64

6 8 0.36

Fax ¼ 0:628� ð2067� 1287:878788Þ2ð1324Þ2 � 3:14� 81:75

� 42þ 61:5þ 102

3

� �� ð2� 0:950� 1Þ � 10

� ð0:950� 1:414Þ2 � 10�6N

7 10 �1.52

8 15 �5.2

¼ 0:628� 7:087� 1012

1; 752; 976� 256:695� 96:5� 9� 1:805� 10�6

¼ 0:628� 4042893:149� 256:965� 96:5� 9� 1:805� 10�6

¼ 1021669:773

Percentage Error ¼ Experimental Value� Theoretical Value

Theoretical Value

� 100 ð7:2Þ

P:E: ¼ 1100558:131� 1021669:773

1021669:773� 100

P:E: ¼ 7:72%

Remaining percentage error values of transformer displacedmodel are shown in Table 1.

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Short Circuit Stress Analysis 11

8. Conclusions

The results of mechanical forces generated due to prolongedhigh currents in power transformer windings have been evalu-

ated. High temperatures generated inside transformer maypuncture are insulation which causes breakdown. As powertransformer is very expensive power system apparatus is

needed to be protected with first priority. That is why its fail-ure is avoided and comprehensive analysis is done to cater alldrastic situations which may cause its complete failure. Thisresearch will enable the transformer manufacturers for careful

design of transformer and the power utility authorities toensure its safe operation in power system.

References

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and Simulation, Islamabad Pakistan, November 2013, 2013.

[3] Georgio Bertagnolli, Short-Circuit Duty of Power

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[4] IEC 60076 Part 5, 2000-07, Power Transformers – Ability to

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[5] D. Meeker, Finite Element Method Magnetics-Version 4.2,

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(1973) 682–689.

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[9] M.R. Patel, Dynamic response of power transformers under

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Further reading

[14] R.A. Kurtz, Comparison of mechanical strengths of three

materials used as pressure plates in oil-filled transformers, in:

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Electrical Manufacturing and Coil Winding Conference,

October 1993, 1993, pp. 519–523.

ing FEM in Power Transformer on H-V Winding Displaced Vertically & Hor-